An isospectral transformation between Hessenberg matrix and Hessenberg-bidiagonal matrix pencil without using subtraction
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866916717578420224 |
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| author | Kobayashi, Katsuki Maeda, Kazuki Tsujimoto, Satoshi |
| author_facet | Kobayashi, Katsuki Maeda, Kazuki Tsujimoto, Satoshi |
| contents | We introduce an eigenvalue-preserving transformation algorithm from the generalized eigenvalue problem by matrix pencil of the upper and the lower bidiagonal matrices into a standard eigenvalue problem while preserving sparsity, using the theory of orthogonal polynomials. The procedure is formulated without subtraction, which causes numerical instability. Furthermore, the algorithm is discussed for the extended case where the upper bidiagonal matrix is of Hessenberg type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11577 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An isospectral transformation between Hessenberg matrix and Hessenberg-bidiagonal matrix pencil without using subtraction Kobayashi, Katsuki Maeda, Kazuki Tsujimoto, Satoshi Numerical Analysis Spectral Theory Exactly Solvable and Integrable Systems 15A18, 37K60, 39A36, 42C05, 65F15 We introduce an eigenvalue-preserving transformation algorithm from the generalized eigenvalue problem by matrix pencil of the upper and the lower bidiagonal matrices into a standard eigenvalue problem while preserving sparsity, using the theory of orthogonal polynomials. The procedure is formulated without subtraction, which causes numerical instability. Furthermore, the algorithm is discussed for the extended case where the upper bidiagonal matrix is of Hessenberg type. |
| title | An isospectral transformation between Hessenberg matrix and Hessenberg-bidiagonal matrix pencil without using subtraction |
| topic | Numerical Analysis Spectral Theory Exactly Solvable and Integrable Systems 15A18, 37K60, 39A36, 42C05, 65F15 |
| url | https://arxiv.org/abs/2212.11577 |